A rubber ball dropped from a height of 1 m bounces (after hitting the floor) several times, losing 10% of its kinetic energy in each bounce.

At a height of 1 m, the potential energy of the ball is m*g*1 where m is the mass of the ball. After it is dropped and it reaches the ground the energy in the ball is in the form of kinetic energy equal to (1/2)*m*v^2.

There is a loss of 10% after the first bounce and after the second bounce the kinetic energy of the ball is (1/2)*m*v^2*(0.9)^2

This is equivalent to the potential energy at a height 1*0.9^2 = .81 m.

**The maximum height of the ball after the second bounce is 0.81 m**

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